Final answer:
To calculate P( z < 1.60 or z > 2.50) for a standard normal distribution, we identify the areas under the curve for z-scores 1.60 and 2.50 using the z-table and add them together.
Step-by-step explanation:
The question asks for P( z < 1.60 or z > 2.50) with the standard deviation being 1 and the mean being 0, which indicates that we're dealing with a standard normal distribution (Z ~ N(0, 1)). To find this probability, we look at a z-table or use statistical software to find the areas under the curve for both sections of the distribution.
To find the probability of z being less than 1.60, we look up the z-score of 1.60 in the z-table, which gives us the area to the left of 1.60. To find the probability of z being greater than 2.50, we look up the z-score of 2.50 and subtract this value from 1, because we want the area in the tail, to the right of 2.50. Finally, we add these two probabilities together to get the total area/probability for our criteria.